Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

long long int N, p[364364], id[364364], dp[364364], x, i;

int main(){
    iota(p, p + 364364, 1);
    scanf("%lld", &N);
    for(; i < N; ++i){
        scanf("%lld", p + i);
        id[p[i]] = i;
    }
    dp[N] = 0;
    x = N;
    for(; --i;){
        if(dp[i + 1]){
            dp[i] = dp[i + 1];
            if((id[i] < id[i + 1]) ^ (id[i + 1] < id[x]) ^ (id[x] < id[i])){
                ++dp[i];
                x = i + 1;
            }
        }else{
            dp[i] = dp[i + 1] + ((id[i] > id[i + 1]) ? 1 : 0);
            if(id[i] < id[i + 1])--x;
        }
    }
    cout << dp[1] << endl;
    return 0;
}